Lots of Squares
Describe the properties of a square
Work systematically when problem solving
Devise and use problem solving strategies (act it out, draw a picture)
Use equipment appropriately
This problem explores the concept of "squareness". It reinforces the understanding that a square has 4 equal sides and 4 right angles. The students need to recognise that a square is not always 
but may be 
Problem
How many squares can you find that have dots from this array as their corners?
Teaching sequence
- Introduce the problem as a "treasure hunt". How many squares can be made on this board (or grid)? Let the search begin!
- Ask the students, in pairs, to make a square on the geoboard with a rubberband (or draw one on the dot paper). It can be any size and in any location.
- Share the squares found by the class. Notice whether the squares displayed are different by size, location or both.
- Pose the problem: How many squares do you think that you can find?
- As the students work ask:
How do you know when something is a square?
What did you find out during this activity?
Are you organising your search for the squares? How? - Share answers. If there are different answers look at why this is so. Get the students to share the ways that they organised their search.
Extension
Squares in a 5x5 geoboard or copymaster 5 x 5 dot paper
Other contexts for the problem
Solution
18 squares
| Size of square | Number |
| 1x1 | 9 |
| 2x2 | 4 |
| 3x3 | 1 |
| tilted (one dot enclosed) | 4 |
| tilted (4 dots enclosed) | 2 |
Some students may notice that there is a pattern in the number of the non-tilted squares (1, 22, 32)
Extension:
Solution:
| Attachment | Size |
|---|---|
| Lots of Squares.pdf | 34.21 KB |
| Lots of Squares dot paper Maori.pdf | 47.49 KB |
| Lots of Squares dot paper.pdf | 21.11 KB |
| Lots of Squares dot paper 5 x5.pdf | 30.9 KB |
Similar Resources
Flip's Flag
apply the angle properties of squares, rectangles and triangles
use fractions to express the relationships between the areas of rectangles, squares and triangles
devise and use problem solving strategies to explore situations mathematically (be systematic).
Mosaic Puzzles
Join shapes together to form other shapes
Identify and describe shapes
Devise and use problem solving strategies to explore situations mathematically (guess and check).
How Many Numbers ?
Devise and use problem solving strategies to explore situations mathematically (be systematic, make a list).
My Son is Naughty
Find factors of numbers
Work systematically
Use logic to explain away certain possible number combinations.
Time Problems
Understand how positive and negative numbers can be used in an unusual practical problem.
Devise and use problem solving strategies to explore situations mathematically (guess and check, be systematic, look for patterns, draw a diagram, make a table, use algebra).
